Bose-Hubbard Hamiltonian: Quantum Chaos approach

We discuss applications of the theory of Quantum Chaos to one of the paradigm models of many-body quantum physics – the Bose-Hubbard model, which describes, in particular, interacting ultracold Bose atoms in an optical lattice. After preliminary, pure quantum analysis of the system we introduce the classical counterpart of the Bose-Hubbard model and the governing semiclassical equations of motion. We analyze these equations for the problem of Bloch oscillations of cold atoms where a number of experimental results are available. The review is written for non-experts and can be viewed as an introduction to the field.